Cornett, who had 70 yards rushing, scored on the ground from 7 and 3 yards and 1 yard. In the fourth quarter, he caught a 12-yard TD pass for the Rebels (2-8, 2-4 Mountain West), who ended a five-game losing streak.
Clayton was 13 of 18 passing 163 yards with no interceptions. He also rushed for 50 yards on 11 carries and caught a pass for 16 yards.
Alvester Alexander led Wyoming (2-8, 0-7) with 92 yards rushing, including a 72-yard run on the game's first play from scrimmage. Austyn Carta-Samuels was 13 of 22 for 108 yards with an interception for the Cowboys, who have lost six straight.
Miami has lost running back Gus Edwards for the entire season because of a left foot injury.
Virginia Tech will wear a decal on its helmets against No. 1 Ohio State on Monday night to honor slain Roanoke television journalists Alison Parker and Adam Ward.
South Carolina football players will wear stickers on their helmets this season to honor the nine people who died in a shooting at Emanuel AME Church in Charleston this past June.
Washington has found its starting quarterback, but coach Chris Petersen said the Huskies will keep that information under wraps until Friday's season opener at No. 23 Boise State.
Joey Counts scored on a 1-yard run on fourth-and-goal with 2 seconds left to give Montana a 38-35 victory over four-time defending FCS champion North Dakota State on Saturday.
Transfer Vernon Adams will be the starting quarterback when Oregon begins its season against Eastern Washington on Sept. 5.